Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
746 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. Q16×#157 | C2 | direct (N × H) |
| 15. C2×C32×Q16 | C4 | semidirect |
| 16. C2×#3756 | C4 | semidirect |
| 17. Q16×C3⋊D3 | C4 | semidirect |
| 19. C2×#3746 | C4 | semidirect |
| 46. C32×Q16 | C2×C4 | semidirect |
| 48. #3756 | C2×C4 | semidirect |
| 50. #3746 | C2×C4 | semidirect |
| 65. C2×#157 | Q16 | direct (N × H) |
| 116. #157 | C2×Q16 | direct (N × H) |
| 128. C2×Q16 | #157 | direct (N × H) |
| 159. C2×C32 | C4×Q16 | semidirect |
| 161. C3⋊D3 | C4×Q16 | semidirect |
| 178. Q16 | C2×#157 | direct (N × H) |
| 203. C32 | C2×C4×Q16 | semidirect |
| 253. C2 | Q16×#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| C2×Q16×C3⋊D3 | 2 |
| C2×#63784 | 2 |
| Q16×#157 | 2 |
| C2×#63769 | 2 |
| C2×C8×#157 | 2 |
| C2×C4×Q16 | 9 |